Morris "Moe" Koffman was born on December 28, 1928 in Toronto, Canada. At the age of nine he began his musical studies in his native city, studying violin. He attended the Toronto Conservatory of Music, where he was a student of Samuel Dolin.

Dropping out of school when he found work performing in dance bands, in 1950, he moved to the United States, where he played with big bands including those of Sonny Dunham and Jimmy Dorsey. In 1955, he returned to Toronto where he formed a quartet and later a quintet…